Homogenization of a stochastic nonlinear reaction-diffusion equation with a large reaction term: The almost periodic framework

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:394

Article

Razafimandimby, Paul Andre²  Sango, Mamadou²  Woukeng, Jean Louis^1,2 

[1] Univ Dschang, Dept Math & Comp Sci, Dschang, Cameroon

[2] Univ Pretoria, Dept Math & Appl Math, ZA-0002 Pretoria, South Africa

关键词: Stochastic homogenization;    Almost periodic;    Stochastic reaction-diffusion equations;    Wiener process;   

DOI  :  10.1016/j.jmaa.2012.04.046

来源: Elsevier

【 摘 要 】

Homogenization of a stochastic nonlinear reaction-diffusion equation with a large nonlinear term is considered. Under a general Besicovitch almost periodicity assumption on the coefficients of the equation we prove that the sequence of solutions of the said problem converges in probability towards the solution of a rather different type of equation, namely, the stochastic nonlinear convection-diffusion equation which we explicitly derive in terms of appropriate functionals. We study some particular cases such as the periodic framework, and many others. This is achieved under a suitable generalized concept of E-convergence for stochastic processes. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free